Search results for: Fourier series

Authors: Saad Al-Baddai, Karema Al-Subari, Elmar Lang, Bernd Ludwig

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Empirical mode decomposition (EMD), a new data-driven of time-series decomposition, has the advantage of supposing that a time series is non-linear or non-stationary, as is implicitly achieved in Fourier decomposition. However, the EMD suffers of mode mixing problem in some cases. The aim of this paper is to present a solution for a common type of signals causing of EMD mode mixing problem, in case a signal suffers of an intermittency. By an artificial example, the solution shows superior performance in terms of cope EMD mode mixing problem comparing with the conventional EMD and Ensemble Empirical Mode decomposition (EEMD). Furthermore, the over-sifting problem is also completely avoided; and computation load is reduced roughly six times compared with EEMD, an ensemble number of 50.

Keywords: empirical mode decomposition (EMD), mode mixing, sifting process, over-sifting

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Authors: Felix Givois, Nicolas R. Gauger, Matthias Kabel

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The efficient digital material characterization is of great interest to many fields of application. It consists of the following three steps. First, a 3D reconstruction of 2D scans must be performed. Then, the resulting gray-value image of the material sample is enhanced by image processing methods. Finally, partial differential equations (PDE) are solved on the segmented image, and by averaging the resulting solutions fields, effective properties like stiffness or conductivity can be computed. Due to the high resolution of current CT images, the latter is typically performed with matrix-free solvers. Among them, a solver that uses the explicit formula of the Green-Eshelby operator in Fourier space has been proposed by Moulinec and Suquet. Its algorithmic, most complex part is the Fast Fourier Transformation (FFT). In our talk, we will discuss the potential quantum advantage that can be obtained by replacing the FFT with the Quantum Fourier Transformation (QFT). We will especially show that the data transfer for noisy intermediate-scale quantum (NISQ) devices can be improved by using appropriate boundary conditions for the PDE, which also allows using semi-classical versions of the QFT. In the end, we will compare the results of the QFT-based algorithm for simple geometries with the results of the FFT-based homogenization method.

Keywords: most likelihood amplitude estimation (MLQAE), numerical homogenization, quantum Fourier transformation (QFT), NISQ devises

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Authors: C. Slim

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Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary non-seasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Keywords: stationarity, unit root tests, economic time series, ADF tests

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi

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In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reflected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system.

Keywords: time series, fluctuation in statistical characteristics, optimal learning, change-point algorithm

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Authors: K. Subbaiah

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Friction stir welding is a solid state welding process. Friction stir welding process eliminates the defects found in fusion welding processes. It is environmentally friend process. 5000 and 6000 series aluminum alloys are widely used in the transportation industries. The Al-Mg-Mn (5000) and Al-Mg-Si (6000) alloys are preferably offer best combination of use in Marine construction. The medium strength and high corrosion resistant 5000 series alloys are the aluminum alloys, which are found maximum utility in the world. In this review, the tool pin profile, process parameters such as hardness, yield strength and tensile strength, and microstructural evolution of friction stir welding of Al-Mg alloys 5000 Series and 6000 series have been discussed.

Keywords: 5000 series and 6000 series Al alloys, friction stir welding, tool pin profile, microstructure and properties

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

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This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: reconfigurable, fast Fourier transform (FFT), single-path delay feedback (SDF), 3GPP-LTE

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Evren Şar İşbilen

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As it is known, the movies and tv series are occupying a large part in the daily lives of adults and children in our era. In this connection, in the present study, the most popular historical TV series of recent years in Turkey, “Muhteşem Yüzyıl” (The Magnificent Century), was selected as the sample for the data collection in order to explore the perception of history of university students’. The data collected was analyzed bothqualitatively and quantitatively. The findings discussed in relation to the possible educative effects of historical non-educational TV series and movies on students' perceptions related to history. Additionally, suggestions were made regarding to the utilization of non-educational TV series or movies in education in a positive way.

Keywords: education, history, movies, teacher candidates

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Authors: Ioannis Andrianakis, Vasileios Gkatas, Nikos Eleftheriadis, Alexios Ellinidis, Ermioni Avramidou

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pscmsForecasting is an open-source web service that implements a variety of time series forecasting algorithms and exposes them to the user via the ubiquitous HTTP protocol. It allows developers to enhance their applications by adding time series forecasting functionalities through an intuitive and easy-to-use interface. This paper provides some background on time series forecasting and gives details about the implemented algorithms, aiming to enhance the end user’s understanding of the underlying methods before incorporating them into their applications. A detailed description of the web service’s interface and its various parameterizations is also provided. Being an open-source project, pcsmsForecasting can also be easily modified and tailored to the specific needs of each application.

Keywords: time series, forecasting, web service, open source

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Authors: Di Yao, Gunther Prokop, Kay Buttner

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Dynamic parameters, including the center of gravity, mass and inertia moments of vehicle, play an essential role in vehicle simulation, collision test and real-time control of vehicle active systems. To identify the important vehicle dynamic parameters, a systematic parameter identification procedure is studied in this work. In the first step of the procedure, a conceptual parallel manipulator (virtual test rig), which possesses three rotational degrees-of-freedom, is firstly proposed. To realize kinematic characteristics of the conceptual parallel manipulator, the kinematic analysis consists of inverse kinematic and singularity architecture is carried out. Based on the Euler's rotation equations for rigid body dynamics, the dynamic model of parallel manipulator and derivation of measurement matrix for parameter identification are presented subsequently. In order to reduce the sensitivity of parameter identification to measurement noise and other unexpected disturbances, a parameter optimization process of searching for optimal exciting trajectory of parallel manipulator is conducted in the following section. For this purpose, the 321-Euler-angles defined by parameterized finite-Fourier-series are primarily used to describe the general exciting trajectory of parallel manipulator. To minimize the condition number of measurement matrix for achieving better parameter identification accuracy, the unknown coefficients of parameterized finite-Fourier-series are estimated by employing an iterative algorithm based on MATLAB®. Meanwhile, the iterative algorithm will ensure the parallel manipulator still keeps in an achievable working status during the execution of optimal exciting trajectory. It is showed that the proposed procedure and methods in this work can effectively identify the vehicle dynamic parameters and could be an important application of parallel manipulator in the fields of parameter identification and test rig development.

Keywords: parameter identification, parallel manipulator, singularity architecture, dynamic modelling, exciting trajectory

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Authors: Temidayo Otunniyi

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This paper presents a low computational channelization algorithm for the multi-standards platform using poly phase implementation of a critically sampled hybrid Trigonometry generalized Discrete Fourier Transform, (HGDFT). An HGDFT channelization algorithm exploits the orthogonality of two trigonometry Fourier functions, together with the properties of Quadrature Mirror Filter Bank (QMFB) and Exponential Modulated filter Bank (EMFB), respectively. HGDFT shows improvement in its implementation in terms of high reconfigurability, lower filter length, parallelism, and medium computational activities. Type 1 and type 111 poly phase structures are derived for real-valued HGDFT modulation. The design specifications are decimated critically and over-sampled for both single and multi standards receiver platforms. Evaluating the performance of oversampled single standard receiver channels, the HGDFT algorithm achieved 40% complexity reduction, compared to 34% and 38% reduction in the Discrete Fourier Transform (DFT) and tree quadrature mirror filter (TQMF) algorithm. The parallel generalized discrete Fourier transform (PGDFT) and recombined generalized discrete Fourier transform (RGDFT) had 41% complexity reduction and HGDFT had a 46% reduction in oversampling multi-standards mode. While in the critically sampled multi-standard receiver channels, HGDFT had complexity reduction of 70% while both PGDFT and RGDFT had a 34% reduction.

Keywords: software defined radio, channelization, critical sample rate, over-sample rate

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Authors: Dahi Ghareab Abdelsalam Ibrahim, R. H. Bakr

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Ionizing radiation, such as gamma radiation and X-rays, has many applications in medical diagnoses and cancer treatment. In this paper, we used the windowed Fourier transform to extract the complex image of the deformed red blood cells. The real values of the complex image are used to extract the best fitting of the deformed cell boundary. Male albino rats are irradiated by γ-rays from ⁶⁰Co. The male albino rats are anesthetized with ether, and then blood samples are collected from the eye vein by heparinized capillary tubes for studying the radiation-damaging effect in-vivo by the proposed windowed Fourier transform. The peripheral blood films are prepared according to the Brown method. The peripheral blood film is photographed by using an Automatic Image Contour Analysis system (SAMICA) from ELBEK-Bildanalyse GmbH, Siegen, Germany. The SAMICA system is provided with an electronic camera connected to a computer through a built-in interface card, and the image can be magnified up to 1200 times and displayed by the computer. The images of the peripheral blood films are then analyzed by the windowed Fourier transform method to extract the precise deformation from the best fitting. Based on accurate deformation evaluation of the red blood cells, diseases can be diagnosed in their primary stages.

Keywords: windowed Fourier transform, red blood cells, phase wrapping, Image processing

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Authors: Lienjang Zeite

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Over the past few years, Turkish and Indian series have been distributed worldwide to countless households and have found ardent followers across different age group. The series have captured numerous hearts. Turkish and Indian series have become not only one of the best means of entertainment and relaxation but also a platform to learn and appreciate shared emotions and social messages. The popularity of the series has created a kind of interest in representing human emotions and stories like never before. The demands for such series have totally shifted the entertainment industry at a new level. The interest and vibe created by the series have had impacts on various departments spanning from technology to the fashion industry and it has also become the bridge to connect viewers across the globe. The series have amassed avid admirers who find solace in the beautiful visual representations of human relationships whether it is of lovers, family or friendship. The influence of Turkish and Indian series in many parts of the world has created a cultural phenomenon that has taken viewers beyond cultural and language differences. From China to Latin America, Arab countries and the Caucasus region, the series have been accepted and loved by millions of viewers. It has captivated audiences ranging from grandmothers to teenagers. Issues like language barrier are easily solved by means of translation or dubbing making it easier to understand and enjoy the series. Turkey and India are two different countries with their own unique culture and traditions. Both the countries are exporters of series in large scale. The series function as a platform to reveal the plots and shed lights on characters of all kinds. Both the countries produce series that are more or less similar in nature. However, there are also certain issues that are shown in different ways and light. The paper will discuss how emotions are represented in Turkish and Indian series. It will also discuss the ways the series have impacted the art of representing emotions and characters in the digital era. The representation of culture through Turkish and Indian series will be explored as well. The paper will also locate the issue of gender roles and how relationships are forged or abandoned in the series. The issue of character formation and importance of moral factors will be discussed. It will also examine the formula and ingredients of turning human emotions and characters into a much loved series.

Keywords: characters, cultural phenomenon, emotions, Turkish and Indian series

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Authors: Mohammad H. Fattahi

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Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. The noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: chaotic behavior, wavelet, noise reduction, river flow

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Authors: Vineetha Bettaiah, Heggere S. Ranganath

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This paper presents a Hierarchical Piecewise Linear Approximation (HPLA) for the representation of time series data in which the time series is treated as a curve in the time-amplitude image space. The curve is partitioned into segments by choosing perceptually important points as break points. Each segment between adjacent break points is recursively partitioned into two segments at the best point or midpoint until the error between the approximating line and the original curve becomes less than a pre-specified threshold. The HPLA representation achieves dimensionality reduction while preserving prominent local features and general shape of time series. The representation permits course-fine processing at different levels of details, allows flexible definition of similarity based on mathematical measures or general time series shape, and supports time series data mining operations including query by content, clustering and classification based on whole or subsequence similarity.

Keywords: data mining, dimensionality reduction, piecewise linear representation, time series representation

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Authors: Edwin Calderon-Mendoza, Patrick Schweitzer, Serge Weber

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Series arc faults appear frequently and unpredictably in low voltage distribution systems. Many methods have been developed to detect this type of faults and commercial protection systems such AFCI (arc fault circuit interrupter) have been used successfully in electrical networks to prevent damage and catastrophic incidents like fires. However, these devices do not allow series arc faults to be located on the line in operating mode. This paper presents a location algorithm for series arc fault in a low-voltage indoor power line in an AC 230 V-50Hz home network. The method is validated through simulations using the MATLAB software. The fault location method uses electrical parameters (resistance, inductance, capacitance, and conductance) of a 49 m indoor power line. The mathematical model of a series arc fault is based on the analysis of the V-I characteristics of the arc and consists basically of two antiparallel diodes and DC voltage sources. In a first step, the arc fault model is inserted at some different positions across the line which is modeled using lumped parameters. At both ends of the line, currents and voltages are recorded for each arc fault generation at different distances. In the second step, a fault map trace is created by using signature coefficients obtained from Kirchhoff equations which allow a virtual decoupling of the line’s mutual capacitance. Each signature coefficient obtained from the subtraction of estimated currents is calculated taking into account the Discrete Fast Fourier Transform of currents and voltages and also the fault distance value. These parameters are then substituted into Kirchhoff equations. In a third step, the same procedure described previously to calculate signature coefficients is employed but this time by considering hypothetical fault distances where the fault can appear. In this step the fault distance is unknown. The iterative calculus from Kirchhoff equations considering stepped variations of the fault distance entails the obtaining of a curve with a linear trend. Finally, the fault distance location is estimated at the intersection of two curves obtained in steps 2 and 3. The series arc fault model is validated by comparing current registered from simulation with real recorded currents. The model of the complete circuit is obtained for a 49m line with a resistive load. Also, 11 different arc fault positions are considered for the map trace generation. By carrying out the complete simulation, the performance of the method and the perspectives of the work will be presented.

Keywords: indoor power line, fault location, fault map trace, series arc fault

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Authors: A. Djahbar, E. Bounadja, A. Zegaoui, H. Allouache

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In this paper, vector control of a series-connected two-machine drive system fed by a single inverter (CSI/VSI) is presented. The two stator windings of both machines are connected in series while the rotors may be connected to different loads, are called series-connected two-machine drive. Appropriate phase transposition is introduced while connecting the series stator winding to obtain decoupled control the two-machines. The dynamic decoupling of each machine from the group is obtained using the vector control algorithm. The independent control is demonstrated by analyzing the characteristics of torque and speed of each machine obtained via simulation under vector control scheme. The viability of the control techniques is proved using analytically and simulation approach.

Keywords: drives, inverter, multi-phase induction machine, vector control

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Authors: Muhammad Tariq, Hammad Tahir, Fawwad Mahmood Butt

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Purpose: This study attempts to examine the best forecasting methodologies in the time series. The time series forecasting models such as VAR, ARCH and the ARMA are considered for the analysis. Methodology: The Bench Marks or the parameters such as Adjusted R square, F-stats, Durban Watson, and Direction of the roots have been critically and empirically analyzed. The empirical analysis consists of time series data of Consumer Price Index and Closing Stock Price. Findings: The results show that the VAR model performed better in comparison to other models. Both the reliability and significance of VAR model is highly appreciable. In contrary to it, the ARCH model showed very poor results for forecasting. However, the results of ARMA model appeared double standards i.e. the AR roots showed that model is stationary and that of MA roots showed that the model is invertible. Therefore, the forecasting would remain doubtful if it made on the bases of ARMA model. It has been concluded that VAR model provides best forecasting results. Practical Implications: This paper provides empirical evidences for the application of time series forecasting model. This paper therefore provides the base for the application of best time series forecasting model.

Keywords: forecasting, time series, auto regression, ARCH, ARMA

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Authors: Sunil Dehipawala, Aregama Sirisumana, stephan Smith, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden, T. Cheung

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The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, fourier transform, metalloproteins, XANES

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Authors: Seyyd Hossein Jafari-Petroudi, Maryam Pirouz

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This note is devoted to (k; h)-Jacobsthal sequence as a general term of particular series. More formulas for nth term and sum of the first n terms of series that their general terms are (k; h)-Jacobsthal sequence and (k; h)-Jacobsthal-Petroudi sequence are derived. Finally other properties of these sequences are represented.

Keywords: (k, h)-Jacobsthal sequence, (k, h)-Jacobsthal Petroudisequence, recursive relation, sum

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Authors: O. Delage, H. Bencherif, T. Portafaix, A. Bourdier

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The main purpose of time series analysis is to learn about the dynamics behind some time ordered measurement data. Two approaches are used in the literature to get a better knowledge of the dynamics contained in observation data sequences. The first of these approaches concerns time series decomposition, which is an important analysis step allowing patterns and behaviors to be extracted as components providing insight into the mechanisms producing the time series. As in many cases, time series are short, noisy, and non-stationary. To provide components which are physically meaningful, methods such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT) or, more recently, Empirical Adaptive Wavelet Decomposition (EAWD) have been proposed. The second approach is to reconstruct the dynamics underlying the time series as a trajectory in state space by mapping a time series into a set of Rᵐ lag vectors by using the method of delays (MOD). Takens has proved that the trajectory obtained with the MOD technic is equivalent to the trajectory representing the dynamics behind the original time series. This work introduces the singular spectrum decomposition (SSD), which is a new adaptive method for decomposing non-linear and non-stationary time series in narrow-banded components. This method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for the analysis and prediction of time series. As the first step of SSD is to constitute a trajectory matrix by embedding a one-dimensional time series into a set of lagged vectors, SSD can also be seen as a reconstruction method like MOD. We will first give a brief overview of the existing decomposition methods (EMD-EWT-EAWD). The SSD method will then be described in detail and applied to experimental time series of observations resulting from total columns of ozone measurements. The results obtained will be compared with those provided by the previously mentioned decomposition methods. We will also compare the reconstruction qualities of the observed dynamics obtained from the SSD and MOD methods.

Keywords: time series analysis, adaptive time series decomposition, wavelet, phase space reconstruction, singular spectrum analysis

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Authors: Kankeyanathan Kannan

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On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Daniel Fulus Fom, Gau Patrick Damulak

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In this study, the Autoregressive Fractional Integrated Moving Average (ARFIMA) and Jordan Recurrent Neural Network (JRNN) models were employed to model the forecasting performance of the daily turbidity flow of White Clay Creek (WCC). The two methods were applied to the log difference series of the daily turbidity flow series of WCC. The measurements of error employed to investigate the forecasting performance of the ARFIMA and JRNN models are the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The outcome of the investigation revealed that the forecasting performance of the JRNN technique is better than the forecasting performance of the ARFIMA technique in the mean square error sense. The results of the ARFIMA and JRNN models were obtained by the simulation of the models using MATLAB version 8.03. The significance of using the log difference series rather than the difference series is that the log difference series stabilizes the turbidity flow series than the difference series on the ARFIMA and JRNN.

Keywords: auto regressive, mean absolute error, neural network, root square mean error

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Authors: Marwa A. A. Ragab, Hadir M. Maher, Eman I. El-Kimary

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Co-administration of methotrexate (MTX) and aspirin (ASP) can cause a pharmacokinetic interaction and a subsequent increase in blood MTX concentrations which may increase the risk of MTX toxicity. Therefore, it is important to develop a sensitive, selective, accurate and precise method for their simultaneous determination in urine. A new hybrid chemometric method has been applied to the emission response data of the two drugs. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (4-AMP), was developed. Moreover, the acid-catalyzed degradation reaction enables the spectrofluorimetric determination of ASP through the formation of its active metabolite salicylic acid (SA). The proposed chemometric method deals with convolution of emission data using 8-points sin xi polynomials (discrete Fourier functions) after the derivative treatment of these emission data. The first and second derivative curves (D1 & D2) were obtained first then convolution of these curves was done to obtain first and second derivative under Fourier functions curves (D1/FF) and (D2/FF). This new application was used for the resolution of the overlapped emission bands of the degradation products of both drugs to allow their simultaneous indirect determination in human urine. Not only this chemometric approach was applied to the emission data but also the obtained data were subjected to non-parametric linear regression analysis (Theil’s method). The proposed method was fully validated according to the ICH guidelines and it yielded linearity ranges as follows: 0.05-0.75 and 0.5-2.5 µg mL-1 for MTX and ASP respectively. It was found that the non-parametric method was superior over the parametric one in the simultaneous determination of MTX and ASP after the chemometric treatment of the emission spectra of their degradation products. The work combines the advantages of derivative and convolution using discrete Fourier function together with the reliability and efficacy of the non-parametric analysis of data. The achieved sensitivity along with the low values of LOD (0.01 and 0.06 µg mL-1) and LOQ (0.04 and 0.2 µg mL-1) for MTX and ASP respectively, by the second derivative under Fourier functions (D2/FF) were promising and guarantee its application for monitoring the two drugs in patients’ urine samples.

Keywords: chemometrics, emission curves, derivative, convolution, Fourier transform, human urine, non-parametric regression, Theil’s method

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Authors: Jinghui Peng, Shanyu Tang, Jia Li

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Steganalysis seeks to detect the presence of secret data embedded in cover objects, and there is an imminent demand to detect hidden messages in streaming media. This paper shows how a steganalysis algorithm based on Fast Fourier Transform (FFT) can be used to detect the existence of secret data embedded in streaming media. The proposed algorithm uses machine parameter characteristics and a network sniffer to determine whether the Internet traffic contains streaming channels. The detected streaming data is then transferred from the time domain to the frequency domain through FFT. The distributions of power spectra in the frequency domain between original VoIP streams and stego VoIP streams are compared in turn using t-test, achieving the p-value of 7.5686E-176 which is below the threshold. The results indicate that the proposed FFT-based steganalysis algorithm is effective in detecting the secret data embedded in VoIP streaming media.

Keywords: steganalysis, security, Fast Fourier Transform, streaming media

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Authors: Plessen Mogens Graf

Abstract:

Within the context of multivariate time series segmentation, this paper proposes a method inspired by a posteriori optimal trading. After a normalization step, time series are treated channelwise as surrogate stock prices that can be traded optimally a posteriori in a virtual portfolio holding either stock or cash. Linear transaction costs are interpreted as hyperparameters for noise filtering. Trading signals, as well as trading signals obtained on the reversed time series, are used for unsupervised channelwise labeling before a consensus over all channels is reached that determines the final segmentation time instants. The method is model-free such that no model prescriptions for segments are made. Benefits of proposed approach include simplicity, computational efficiency, and adaptability to a wide range of different shapes of time series. Performance is demonstrated on synthetic and real-world data, including a large-scale dataset comprising a multivariate time series of dimension 1000 and length 2709. Proposed method is compared to a popular model-based bottom-up approach fitting piecewise affine models and to a recent model-based top-down approach fitting Gaussian models and found to be consistently faster while producing more intuitive results in the sense of segmenting time series at peaks and valleys.

Keywords: time series segmentation, model-free, trading-inspired, multivariate data

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